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C. J. Quimbay

Publications and source records attributed to C. J. Quimbay.

13 recordsLinked to original sources
arXiv2025

Path Integral for Multiplicative Noise: Generalized Fokker-Planck Equation and Entropy Production Rate in Stochastic Processes With Threshold

This paper introduces a comprehensive extension of the path integral formalism to model stochastic processes with arbitrary multiplicative noise. To do so, Itô diffusive process is generalized by incorporating a multiplicative noise term $(η(t))$ that affects the diffusive coefficient in the stochastic differential equation. Then, using the Parisi-Sourlas method, we estimate the transition probability between states of a stochastic variable $(X(t))$ based on the cumulant generating function $(\mathcal{K}_η)$ of the noise. A parameter $γ\in[0,1]$ is introduced to account for the type of stochastic calculation used and its effect on the Jacobian of the path integral formalism. Next, the Feynman-Kac functional is then employed to derive the Fokker-Planck equation for generalized Itô diffusive processes, addressing issues with higher-order derivatives and ensuring compatibility with known functionals such as Onsager-Machlup and Martin-Siggia-Rose-Janssen-De Dominicis in the white noise case. The general solution for the Fokker-Planck equation is provided when the stochastic drift is proportional to the diffusive coefficient and $\mathcal{K}_η$ is scale-invariant. Finally, the Brownian motion ($BM$), the geometric Brownian motion ($GBM$), the Levy $α$-stable flight ($LF(α)$), and the geometric Levy $α$-stable flight ($GLF(α)$) are simulated with thresholds, providing analytical comparisons for the probability density, Shannon entropy, and entropy production rate. It is found that restricted $BM$ and restricted $GBM$ exhibit quasi-steady states since the rate of entropy production never vanishes. It is also worth mentioning that in this work the $GLF(α)$ is defined for the first time in the literature and it is shown that its solution is found without the need for Itô's lemma.

math-ph↗
arXiv2021

Dynamical symmetry breaking, magnetization and induced charge in graphene: Interplay between magnetic and pseudomagnetic fields

In this paper, we investigate the two competing effects of strains and magnetic fields in single-layer graphene to explore its impact on various phenomena of quantum field theory, such as induced charge density, magnetic catalysis, symmetry breaking, dynamical mass generation and magnetization. We show that the interplay between strains and magnetic fields produces not only a breaking of chiral symmetry, as it happens in QED$_{2+1}$, but also parity and time-reversal symmetry breaking. The last two symmetry breakings are related to the dynamical generation of a Haldane mass term. We find that it is possible to modify the magnetization and the dynamical mass independently for each valley, by strain and varying the external magnetic field. Furthermore, we discover that the presence of a non-zero pseudomagnetic field, unlike the magnetic one, allows us to observe an induced "vacuum" charge and a parity anomaly in strained graphene. Finally, because the combined effect of real and pseudomagnetic fields produces an induced valley polarization, the results presented here may provide new tools to design valleytronic devices.

hep-th↗
arXiv2019

Piketty's second fundamental law of capitalism as an emergent property in a kinetic wealth-exchange model of economic growth

We propose in this work a kinetic wealth-exchange model of economic growth by introducing saving as a non consumed fraction of production. In this new model, which starts also from microeconomic arguments, it is found that economic transactions between pairs of agents leads the system to a macroscopic behavior where total wealth is not conserved and it is possible to have an economic growth which is assumed as the increasing of total production in time. This last macroeconomic result, that we find both numerically through a Monte Carlo based simulation method and analytically in the framework of a mean field approximation, corresponds to the economic growth scenario described by the well known Solow model developed in the economic neoclassical theory. If additionally to the income related with production due to return on individual capital, it is also included the individual labor income in the model, then the Thomas Piketty's second fundamental law of capitalism is found as a emergent property of the system. We consider that the results obtained in this paper shows how Econophysics can help to understand the connection between macroeconomics and microeconomics.

q-fin.GN↗
arXiv2014

Long-range correlations and trends in Colombian seismic time series

We study long-range correlations and trends in time series extracted from the data of seismic events occurred from 1973 to 2011 in a rectangular region that contains mainly all the continental part of Colombia. The long-range correlations are detected by the calculation of the Hurst exponents for the time series of interevent intervals, separation distances, depth differences and magnitude differences. By using a modification of the classical $R/S$ method that has been developed to detect short-range correlations in time series, we find the existence of persistence for all the time series considered except for magnitude differences. We find also, by using the $DFA$ until the third order, that the studied time series are not influenced by trends. Additionally, an analysis of the Hurst exponent as a function of the number of events in the time and the maximum window size is presented.

physics.geo-ph↗
arXiv2014

Canonical quantization of the Dirac oscillator field in (1+1) and (3+1) dimensions

The main goal of this work is to study the Dirac oscillator as a quantum field using the canonical formalism of quantum field theory and to develop the canonical quantization procedure for this system in $(1+1)$ and $(3+1)$ dimensions. This is possible because the Dirac oscillator is characterized by the absence of the Klein paradox and by the completeness of its eigenfunctions. We show that the Dirac oscillator field can be seen as constituted by infinite degrees of freedom which are identified as decoupled quantum linear harmonic oscillators. We observe that while for the free Dirac field the energy quanta of the infinite harmonic oscillators are the relativistic energies of free particles, for the Dirac oscillator field the quanta are the energies of relativistic linear harmonic oscillators.

quant-ph↗
arXiv2014

Dirac equation in low dimensions: The factorization method

We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equation in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the factorization method can be applied. We show that the presence of electric potentials in the Dirac equation leads to a two Klein-Gordon equations including an energy-dependent potential. We then generalize the factorization method for the case of energy-dependent Hamiltonians. Additionally, the shape invariance is generalized for a specific class of energy-dependent Hamiltonians. We also present a condition for the absence of the Klein's paradox (stability of the Dirac sea), showing how Dirac particles in low dimensions can be confined for a wide family of potentials.

quant-ph↗
arXiv2014

Neutrino dispersion relations at finite temperature and density in the Left-Right Symmetric Model

In this work we calculate the most general left-handed neutrino thermal self-energy at one-loop order in perturbation theory using the Mellin summation technique. We perform this calculation in the real-time formalism of quantum field theory at finite temperature and density assuming that there exists an excess of leptons over antileptons in the medium. Thus, we obtain a novel general expression for the left-handed neutrino effective thermal mass which depends on lepton masses, boson masses, leptonic chemical potential and temperature. As an application of these results into the context of the Left-Right Symmetric Model, we calculate the left-handed neutrino dispersion relations and we obtain the corresponding effective thermal masses for the unbroken, parity-broken and fully-broken symmetry phases.

hep-ph↗
arXiv2014

Spreading of wave packets for neutrino oscillations in vacuum

The effects originated in dispersion with time on spreading of wave packets for the time-integrated two-flavor neutrino oscillation probabilities in vacuum are studied in the context of a field theory treatment. The neutrino flavor states are written as superpositions of neutrino mass eigenstates which are described by localized wave packets. This study is performed for the limit of nearly degenerate masses and considering an expansion of the energy until third order in the momentum. We obtain that the time-integrated neutrino oscillation probabilities are suppressed by a factor $1/L^2$ for the transversal and longitudinal dispersion regimes, where $L$ is the distance between the neutrino source and the detector.

hep-ph↗
arXiv2012

Exact solutions of (n + 1)-dimensional Yang-Mills equations in curved space-time

In the context of a semiclassical approach where vectorial gauge fields can be considered as classical fields, we obtain exact static solutions of the SU(N) Yang-Mills equations in a $(n+1)$ dimensional curved space-time, for the cases $n = 1, 2, 3$. As an application of the results obtained for the case $n=3$, we consider the solutions for the anti-de Sitter and Schwarzschild metrics. We show that these solutions have a confining behavior and can be considered as a first step in the study of the corrections of the spectra of quarkonia in a curved background. Since the solutions that we find in this work are valid also for the group U(1), the case $n=2$ is a description of the $(2+1)$ electrodynamics in presence of a point charge. For this case, the solution has a confining behavior and can be considered as an application of the planar electrodynamics in a curved space-time. Finally we find that the solution for the case $n=1$ is invariant under a parity transformation and has the form of a linear confining solution.

hep-th↗
arXiv2012

Majorana neutrino oscillations in vacuum

In the context of a type I seesaw scenario which leads to get light left-handed and heavy right-handed Majorana neutrinos, we obtain expressions for the transition probability densities between two flavor neutrinos in the cases of left-handed and right-handed neutrinos. We obtain these expressions in the context of an approach developed in the canonical formalism of Quantum Field Theory for neutrinos which are considered as superpositions of mass-eigenstate plane waves with specific momenta. The expressions obtained for the left-handed neutrino case after the ultra-relativistic limit is taking lead to the standard probability densities which describe light neutrino oscillations. For the right-handed neutrino case, the expressions describing heavy neutrino oscillations in the non-relativistic limit are different respect to the ones of the standard neutrino oscillations. However, the right-handed neutrino oscillations are phenomenologically restricted as is shown when the propagation of heavy neutrinos is considered as superpositions of mass-eigenstate wave packets.

hep-ph↗
arXiv2011

Cosmological constant in a quantum fluid model

Possible analogies between vacuum state and quantum fluid provide a model to study vacuum energy density induced by thermal corrections, space-time curvature, boundary conditions and quantum back-reaction. We find that vacuum energy density in this quantum fluid model is not naturally of the order of the matter energy density. We show how higher-order corrections in quantum back-reaction can also contribute to vacuum energy density, and how the cosmological expansion is a manifestation of an universe out of mechanical equilibrium. This last fact implies that simple thermodynamic arguments are not enough to explain the cosmological constant problem due to the calculation of the associated vacuum energy density requires first the knowing of the underlying microscopic physics of vacuum.

hep-th↗
arXiv2006

SU(3) Maxwell equations and the classical chromodynamics

We study the equations of motion of the SU(3) Yang-Mills theory. Since the gluons, at scales of the order of 1 $fm$, can be considered as classical fields, we suppose that the gauge fields ($A_μ^a$) of this theory are the gluonic fields and then it is possible to consider the Quantum Chromodynamics in a classical regime. For the case in which the condition $[A_μ^a, A_ρ^a]=0$ is satisfied, we show that the abelian equations of motion of the Classical Chromodynamics (CCD) have the same form as those of the classical electrodynamics without sources. Additionally, we obtain the non-abelian Maxwell equations for the CCD with sources. We observe that there exist electric and magnetic colour fields whose origin is not fermionic. We show as the gluons can be assumed as the sources of the electric and magnetic colour fields. We note that the gluons are the only responsible for the existence of a magnetic colour monopole in the CCD.

hep-th↗